The congruence topology, Grothendieck duality and thin groups

Alexander Lubotzky, Tyakal Nanjundiah Venkataramana

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

This paper answers a question raised by Grothendieck in 1970 on the “Grothendieck closure” of an integral linear group and proves a conjecture of the first author made in 1980. This is done by a detailed study of the congruence topology of arithmetic groups, obtaining along the way, an arithmetic analogue of a classical result of Chevalley for complex algebraic groups. As an application we also deduce a group theoretic characterization of thin subgroups of arithmetic groups.

Original languageEnglish
Pages (from-to)1281-1298
Number of pages18
JournalAlgebra and Number Theory
Volume13
Issue number6
DOIs
StatePublished - 2019

Bibliographical note

Publisher Copyright:
© 2019, Mathematical Sciences Publishers. All rights reserved.

Keywords

  • Congruence subgroup
  • Thin groups

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